/***************************************************************************
  **************************************************************************
  
                Spherical Harmonic Transform Kit 2.7
  
  
   Contact: Peter Kostelec
            geelong@cs.dartmouth.edu
  
  
   Copyright 1997-2003  Sean Moore, Dennis Healy,
                        Dan Rockmore, Peter Kostelec
  
  
   Copyright 2004  Peter Kostelec, Dan Rockmore


     SpharmonicKit is free software; you can redistribute it and/or modify
     it under the terms of the GNU General Public License as published by
     the Free Software Foundation; either version 2 of the License, or
     (at your option) any later version.
  
     SpharmonicKit is distributed in the hope that it will be useful,
     but WITHOUT ANY WARRANTY; without even the implied warranty of
     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     GNU General Public License for more details.
  
     You should have received a copy of the GNU General Public License
     along with this program; if not, write to the Free Software
     Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
  
  
   Commercial use is absolutely prohibited.
  
   See the accompanying LICENSE file for details.
  
  ************************************************************************
  ************************************************************************/


/****

  OUR supermoduli arrays used in FCTs. See Sean's
  thesis for details. The interface function (defined at the
  bottom of this file) is

  const double *get_mods(int n)

  ****/

static const double mod2[2] = {-0.7071067811865475, 0.7071067811865475};

static const double mod4[4] = 
{-0.923879532511287, 0.923879532511287, 0.3826834323650897, 
  -0.3826834323650898};

static const double mod8[8] = 
{-0.98078528040323, 0.98078528040323, 0.1950903220161282, 
  -0.1950903220161283, -0.5555702330196023, 0.555570233019602, 
  0.831469612302545, -0.831469612302545};

static const double mod16[16] = 
{-0.995184726672197, 0.995184726672197, 0.0980171403295607, 
  -0.0980171403295608, -0.6343932841636457, 0.6343932841636453, 
  0.7730104533627369, -0.773010453362737, -0.881921264348355, 
  0.881921264348355, 0.4713967368259978, -0.4713967368259978, 
  -0.2902846772544623, 0.2902846772544622, 0.956940335732209, 
  -0.956940335732209};

static const double mod32[32] =
{-0.998795456205172, 0.998795456205172, 0.04906767432741801, 
  -0.04906767432741814, -0.6715589548470185, 0.6715589548470185, 
  0.7409511253549589, -0.7409511253549593, -0.903989293123443, 
  0.903989293123443, 0.4275550934302819, -0.4275550934302822, 
  -0.33688985339222, 0.3368898533922199, 0.941544065183021, 
  -0.941544065183021, -0.970031253194544, 0.970031253194544, 
  0.2429801799032639, -0.242980179903264, -0.5141027441932219, 
  0.5141027441932216, 0.857728610000272, -0.857728610000272, 
  -0.803207531480645, 0.803207531480645, 0.5956993044924333, 
  -0.5956993044924336, -0.1467304744553617, 0.1467304744553616, 
  0.989176509964781, -0.989176509964781};

static const double mod64[64] =
{-0.999698818696204, 0.999698818696204, 0.02454122852291214, 
  -0.02454122852291227, -0.689540544737067, 0.6895405447370669, 
  0.7242470829514668, -0.7242470829514671, -0.914209755703531, 
  0.914209755703531, 0.4052413140049898, -0.4052413140049899, 
  -0.3598950365349883, 0.3598950365349882, 0.932992798834739, 
  -0.932992798834739, -0.975702130038529, 0.975702130038528, 
  0.2191012401568697, -0.2191012401568698, -0.5349976198870974, 
  0.534997619887097, 0.844853565249707, -0.844853565249707, 
  -0.817584813151584, 0.817584813151584, 0.5758081914178454, 
  -0.5758081914178455, -0.1709618887603014, 0.1709618887603012, 
  0.985277642388941, -0.985277642388941, -0.99247953459871, 0.99247953459871, 
  0.1224106751992162, -0.1224106751992163, -0.6152315905806269, 
  0.6152315905806267, 0.7883464276266061, -0.7883464276266064, 
  -0.870086991108711, 0.870086991108711, 0.492898192229784, 
  -0.4928981922297842, -0.2667127574748984, 0.2667127574748983, 
  0.96377606579544, -0.96377606579544, -0.949528180593037, 0.949528180593037, 
  0.3136817403988914, -0.3136817403988915, -0.4496113296546067, 
  0.4496113296546067, 0.893224301195515, -0.893224301195515, 
  -0.7572088465064847, 0.7572088465064847, 0.6531728429537766, 
  -0.6531728429537769, -0.07356456359966746, 0.07356456359966735, 
  0.99729045667869, -0.99729045667869};

static const double mod128[128] =
{-0.999924701839145, 0.999924701839145, 0.01227153828571982, 
  -0.01227153828571994, -0.698376249408973, 0.6983762494089728, 
  0.7157308252838185, -0.7157308252838188, -0.919113851690058, 
  0.919113851690058, 0.393992040061048, -0.3939920400610481, 
  -0.3713171939518376, 0.3713171939518375, 0.928506080473215, 
  -0.928506080473215, -0.978317370719628, 0.978317370719628, 
  0.2071113761922184, -0.2071113761922186, -0.5453249884220466, 
  0.5453249884220462, 0.838224705554838, -0.838224705554838, 
  -0.824589302785025, 0.824589302785025, 0.5657318107836132, 
  -0.5657318107836132, -0.183039887955141, 0.1830398879551409, 
  0.983105487431216, -0.983105487431216, -0.993906970002356, 
  0.993906970002356, 0.1102222072938831, -0.1102222072938832, 
  -0.6248594881423865, 0.6248594881423863, 0.7807372285720944, 
  -0.7807372285720945, -0.876070094195407, 0.876070094195407, 
  0.4821837720791227, -0.4821837720791229, -0.278519689385053, 
  0.278519689385053, 0.960430519415566, -0.960430519415566, 
  -0.953306040354194, 0.953306040354194, 0.3020059493192281, 
  -0.3020059493192282, -0.4605387109582401, 0.4605387109582402, 
  0.887639620402854, -0.887639620402854, -0.765167265622459, 
  0.765167265622459, 0.6438315428897913, -0.6438315428897915, 
  -0.0857973123444399, 0.0857973123444398, 0.996312612182778, 
  -0.996312612182778, -0.998118112900149, 0.998118112900149, 
  0.06132073630220854, -0.06132073630220866, -0.6624157775901719, 
  0.6624157775901719, 0.7491363945234591, -0.7491363945234594, 
  -0.898674465693954, 0.898674465693954, 0.4386162385385274, 
  -0.4386162385385277, -0.325310292162263, 0.3253102921622629, 
  0.945607325380521, -0.945607325380521, -0.966976471044852, 
  0.966976471044852, 0.2548656596045145, -0.2548656596045146, 
  -0.5035383837257176, 0.5035383837257175, 0.863972856121587, 
  -0.863972856121587, -0.7958369046088836, 0.7958369046088835, 
  0.6055110414043254, -0.6055110414043256, -0.1345807085071262, 
  0.1345807085071261, 0.99090263542778, -0.99090263542778, 
  -0.987301418157858, 0.987301418157858, 0.1588581433338613, 
  -0.1588581433338614, -0.5857978574564389, 0.5857978574564389, 
  0.810457198252595, -0.810457198252595, -0.851355193105265, 
  0.851355193105265, 0.5245896826784687, -0.524589682678469, 
  -0.2310581082806713, 0.2310581082806711, 0.97293995220556, 
  -0.97293995220556, -0.937339011912575, 0.937339011912575, 
  0.3484186802494344, -0.3484186802494345, -0.4164295600976374, 
  0.416429560097637, 0.909167983090523, -0.909167983090523, 
  -0.7326542716724129, 0.7326542716724127, 0.6806009977954531, 
  -0.6806009977954531, -0.03680722294135899, 0.03680722294135887, 
  0.99932238458835, -0.99932238458835};

static const double mod256[256] =
{-0.999981175282601, 0.999981175282601, 0.006135884649154394, 
  -0.006135884649154516, -0.7027547444572254, 0.7027547444572252, 
  0.7114321957452165, -0.7114321957452165, -0.921514039342042, 
  0.921514039342042, 0.3883450466988262, -0.3883450466988263, 
  -0.3770074102164183, 0.3770074102164182, 0.926210242138311, 
  -0.926210242138311, -0.97956976568544, 0.97956976568544, 
  0.2011046348420918, -0.2011046348420919, -0.5504579729366049, 
  0.5504579729366048, 0.83486287498638, -0.83486287498638, 
  -0.828045045257756, 0.828045045257756, 0.5606615761973359, 
  -0.5606615761973361, -0.1890686641498063, 0.1890686641498062, 
  0.981963869109555, -0.981963869109555, -0.994564570734255, 
  0.994564570734255, 0.1041216338720546, -0.1041216338720547, 
  -0.6296382389149271, 0.629638238914927, 0.7768884656732322, 
  -0.7768884656732325, -0.879012226428634, 0.879012226428634, 
  0.476799230063322, -0.4767992300633223, -0.2844075372112718, 
  0.2844075372112717, 0.958703474895872, -0.958703474895872, 
  -0.955141168305771, 0.955141168305771, 0.2961508882436238, 
  -0.2961508882436239, -0.4659764957679661, 0.465976495767966, 
  0.884797098430938, -0.884797098430938, -0.7691033376455798, 
  0.7691033376455795, 0.6391244448637758, -0.6391244448637759, 
  -0.0919089564971327, 0.0919089564971326, 0.99576741446766, 
  -0.99576741446766, -0.998475580573295, 0.998475580573295, 
  0.05519524434968992, -0.05519524434969004, -0.6669999223036376, 
  0.6669999223036374, 0.7450577854414659, -0.7450577854414661, 
  -0.901348847046022, 0.901348847046022, 0.433093818853152, 
  -0.433093818853152, -0.3311063057598764, 0.3311063057598763, 
  0.94359345816196, -0.94359345816196, -0.968522094274417, 0.968522094274417, 
  0.2489276057457201, -0.2489276057457203, -0.5088301425431072, 
  0.5088301425431072, 0.860866938637767, -0.860866938637767, 
  -0.799537269107905, 0.799537269107905, 0.6006164793838687, 
  -0.600616479383869, -0.1406582393328492, 0.1406582393328491, 
  0.990058210262297, -0.990058210262297, -0.988257567730749, 
  0.988257567730749, 0.1527971852584433, -0.1527971852584434, 
  -0.5907597018588743, 0.5907597018588741, 0.806847553543799, 
  -0.806847553543799, -0.8545579883654, 0.8545579883654, 0.5193559901655897, 
  -0.5193559901655897, -0.2370236059943673, 0.2370236059943672, 
  0.971503890986252, -0.971503890986252, -0.93945922360219, 0.93945922360219, 
  0.3426607173119943, -0.3426607173119944, -0.4220002707997998, 
  0.4220002707997998, 0.906595704514915, -0.906595704514915, 
  -0.7368165688773699, 0.7368165688773698, 0.6760927035753159, 
  -0.6760927035753161, -0.04293825693494096, 0.04293825693494084, 
  0.999077727752645, -0.999077727752645, -0.999529417501093, 
  0.999529417501093, 0.03067480317663646, -0.03067480317663658, 
  -0.6850836677727005, 0.6850836677727001, 0.7284643904482252, 
  -0.7284643904482254, -0.91170603200543, 0.91170603200543, 
  0.4108431710579038, -0.4108431710579039, -0.3541635254204905, 
  0.3541635254204904, 0.935183509938948, -0.935183509938948, 
  -0.974339382785576, 0.974339382785576, 0.2250839113597927, 
  -0.2250839113597927, -0.5298036246862949, 0.5298036246862946, 
  0.848120344803297, -0.848120344803297, -0.814036329705948, 
  0.814036329705948, 0.5808139580957644, -0.5808139580957647, 
  -0.1649131204899701, 0.1649131204899699, 0.986308097244599, 
  -0.986308097244599, -0.9917097536691, 0.9917097536691, 0.1284981107937931, 
  -0.1284981107937932, -0.6103828062763095, 0.6103828062763095, 
  0.7921065773002122, -0.7921065773002124, -0.867046245515693, 
  0.867046245515693, 0.4982276669727816, -0.498227666972782, 
  -0.2607941179152756, 0.2607941179152755, 0.965394441697689, 
  -0.96539444169769, -0.947585591017741, 0.947585591017741, 
  0.3195020308160156, -0.3195020308160157, -0.4441221445704293, 
  0.4441221445704292, 0.895966249756185, -0.895966249756185, 
  -0.7531867990436126, 0.7531867990436125, 0.6578066932970785, 
  -0.6578066932970788, -0.06744391956366412, 0.067443919563664, 
  0.997723066644192, -0.997723066644192, -0.996820299291166, 
  0.996820299291166, 0.07968243797143002, -0.07968243797143014, 
  -0.6485144010221126, 0.6485144010221124, 0.7612023854842617, 
  -0.7612023854842618, -0.890448723244758, 0.890448723244758, 
  0.4550835871263438, -0.4550835871263439, -0.307849640041535, 
  0.3078496400415349, 0.951435020969008, -0.951435020969008, 
  -0.962121404269042, 0.962121404269042, 0.2726213554499488, 
  -0.272621355449949, -0.4875501601484361, 0.4875501601484357, 
  0.87309497841829, -0.87309497841829, -0.7845565971555754, 
  0.7845565971555751, 0.6200572117632892, -0.6200572117632892, 
  -0.1163186309119049, 0.1163186309119047, 0.993211949234795, 
  -0.993211949234795, -0.984210092386929, 0.984210092386929, 
  0.1770042204121487, -0.1770042204121489, -0.5707807458869674, 
  0.5707807458869672, 0.821102514991105, -0.821102514991105, 
  -0.841554977436898, 0.841554977436898, 0.5401714727298929, 
  -0.540171472729893, -0.2131103199160913, 0.2131103199160913, 
  0.977028142657754, -0.977028142657754, -0.930766961078984, 
  0.930766961078984, 0.3656129978047739, -0.365612997804774, 
  -0.3996241998456468, 0.3996241998456467, 0.916679059921043, 
  -0.916679059921043, -0.7200025079613816, 0.7200025079613816, 
  0.6939714608896538, -0.693971460889654, -0.01840672990580482, 
  0.01840672990580469, 0.999830581795824, -0.999830581795823};

static const double mod512[512] = 
{-0.999995293809576, 0.999995293809576, 0.003067956762966015, 
  -0.003067956762966138, -0.704934080375905, 0.7049340803759049, 
  0.7092728264388655, -0.7092728264388657, -0.922701128333879, 
  0.922701128333879, 0.3855160538439189, -0.385516053843919, 
  -0.3798472089240511, 0.379847208924051, 0.925049240782677, 
  -0.925049240782677, -0.980182135968117, 0.980182135968117, 
  0.1980984107179536, -0.1980984107179537, -0.5530167055800276, 
  0.5530167055800274, 0.833170164701913, -0.833170164701913, 
  -0.829761233794523, 0.829761233794523, 0.5581185312205561, 
  -0.5581185312205563, -0.1920803970498924, 0.1920803970498923, 
  0.981379193313755, -0.981379193313755, -0.994879330794806, 
  0.994879330794806, 0.1010698627548277, -0.1010698627548278, 
  -0.6320187359398091, 0.632018735939809, 0.7749531065948739, 
  -0.7749531065948739, -0.880470889052161, 0.880470889052161, 
  0.47410021465055, -0.4741002146505501, -0.2873474595447296, 
  0.2873474595447294, 0.957826413027533, -0.957826413027533, 
  -0.956045251349996, 0.956045251349996, 0.2932191626942586, 
  -0.2932191626942587, -0.468688822035828, 0.4686888220358278, 
  0.883363338665732, -0.883363338665732, -0.7710605242618139, 
  0.7710605242618135, 0.6367618612362844, -0.6367618612362844, 
  -0.0949634953296391, 0.0949634953296389, 0.995480755491927, 
  -0.995480755491927, -0.998640218180265, 0.998640218180265, 
  0.05213170468028319, -0.05213170468028333, -0.6692825883466362, 
  0.6692825883466358, 0.7430079521351218, -0.7430079521351218, 
  -0.902673318237259, 0.902673318237259, 0.4303264813400828, 
  -0.4303264813400827, -0.3339996514420095, 0.3339996514420094, 
  0.942573197601447, -0.942573197601447, -0.969281235356549, 
  0.969281235356549, 0.2459550503357945, -0.2459550503357946, 
  -0.5114688504379706, 0.5114688504379704, 0.859301818357008, 
  -0.859301818357008, -0.80137617172314, 0.80137617172314, 
  0.5981607069963422, -0.5981607069963424, -0.1436950331502946, 
  0.1436950331502945, 0.989622017463201, -0.989622017463201, 
  -0.988721691960324, 0.988721691960324, 0.1497645346773215, 
  -0.1497645346773216, -0.5932322950397998, 0.5932322950397998, 
  0.805031331142964, -0.805031331142964, -0.856147328375194, 
  0.856147328375195, 0.5167317990176496, -0.51673179901765, 
  -0.2400030224487415, 0.2400030224487414, 0.97077214072895, 
  -0.97077214072895, -0.940506070593268, 0.940506070593268, 
  0.3397768844068269, -0.339776884406827, -0.4247796812091088, 
  0.4247796812091088, 0.905296759318119, -0.905296759318119, 
  -0.7388873244606151, 0.738887324460615, 0.6738290003787561, 
  -0.6738290003787562, -0.04600318213091465, 0.04600318213091452, 
  0.998941293186857, -0.998941293186857, -0.999618822495179, 
  0.999618822495179, 0.02760814577896569, -0.02760814577896582, 
  -0.6873153408917592, 0.6873153408917592, 0.7263591550843458, 
  -0.726359155084346, -0.912962190428398, 0.912962190428398, 
  0.4080441628649786, -0.4080441628649788, -0.35703096123343, 
  0.35703096123343, 0.934092550404259, -0.934092550404259, 
  -0.975025345066994, 0.975025345066994, 0.2220936209732035, 
  -0.2220936209732036, -0.5324031278771981, 0.5324031278771978, 
  0.846490938774052, -0.846490938774052, -0.815814410806734, 
  0.815814410806734, 0.5783137964116555, -0.5783137964116556, 
  -0.1679382949747312, 0.1679382949747311, 0.985797509167568, 
  -0.985797509167568, -0.992099313142192, 0.992099313142192, 
  0.1254549834115461, -0.1254549834115462, -0.6128100824294097, 
  0.6128100824294097, 0.79023022143731, -0.7902302214373102, 
  -0.868570705971341, 0.868570705971341, 0.4955652618257723, 
  -0.4955652618257726, -0.2637546789748315, 0.2637546789748314, 
  0.964589793289813, -0.964589793289813, -0.94856134991573, 0.94856134991573, 
  0.3165933755561658, -0.3165933755561658, -0.4468688401623744, 
  0.446868840162374, 0.894599485631383, -0.894599485631383, 
  -0.7552013768965366, 0.7552013768965363, 0.6554928529996154, 
  -0.6554928529996155, -0.07050457338961401, 0.07050457338961391, 
  0.997511456140303, -0.997511456140303, -0.997060070339483, 
  0.997060070339483, 0.0766238613920315, -0.07662386139203161, 
  -0.650846684996381, 0.6508466849963808, 0.759209188978388, 
  -0.7592091889783881, -0.891840709392343, 0.891840709392343, 
  0.452349587233771, -0.452349587233771, -0.3107671527496115, 
  0.3107671527496114, 0.950486073949482, -0.950486073949482, 
  -0.962953266873684, 0.962953266873684, 0.2696683255729151, 
  -0.2696683255729152, -0.4902264832882912, 0.4902264832882912, 
  0.871595086655951, -0.871595086655951, -0.786455213599086, 
  0.7864552135990858, 0.6176473079378038, -0.617647307937804, 
  -0.1193652148109913, 0.1193652148109912, 0.992850414459865, 
  -0.992850414459865, -0.984748501801904, 0.984748501801904, 
  0.1739838733874637, -0.1739838733874639, -0.5732971666980423, 
  0.5732971666980421, 0.819347520076797, -0.819347520076797, 
  -0.843208239641846, 0.843208239641845, 0.5375870762956456, 
  -0.5375870762956456, -0.2161067970762196, 0.2161067970762195, 
  0.976369731330021, -0.976369731330021, -0.931884265581668, 
  0.931884265581668, 0.3627557243673971, -0.3627557243673972, 
  -0.4024346508594185, 0.4024346508594184, 0.915448716088268, 
  -0.915448716088268, -0.7221281939292154, 0.7221281939292153, 
  0.6917592583641577, -0.6917592583641579, -0.02147408027546961, 
  0.02147408027546948, 0.999769405351215, -0.999769405351215, 
  -0.999882347454212, 0.999882347454212, 0.0153392062849881, 
  -0.01533920628498822, -0.6961771314914631, 0.696177131491463, 
  0.7178700450557315, -0.7178700450557317, -0.91790077562139, 
  0.91790077562139, 0.3968099874167103, -0.3968099874167104, 
  -0.3684668299533723, 0.3684668299533722, 0.929640895843181, 
  -0.929640895843181, -0.97767735782451, 0.97767735782451, 
  0.2101118368804696, -0.2101118368804697, -0.542750784864516, 
  0.5427507848645158, 0.839893794195999, -0.839893794195999, 
  -0.822849781375826, 0.822849781375826, 0.5682589526701315, 
  -0.5682589526701316, -0.1800229014056995, 0.1800229014056994, 
  0.98366241921173, -0.98366241921173, -0.993564135520595, 0.993564135520595, 
  0.1132709521775642, -0.1132709521775643, -0.6224612793741501, 
  0.6224612793741499, 0.7826505961665756, -0.7826505961665758, 
  -0.874586652278176, 0.874586652278176, 0.484869248000791, 
  -0.4848692480007912, -0.2755718193109582, 0.2755718193109581, 
  0.961280485811321, -0.961280485811321, -0.952375012719766, 
  0.952375012719766, 0.3049292297354023, -0.3049292297354023, 
  -0.4578133035988773, 0.4578133035988771, 0.889048355854665, 
  -0.889048355854665, -0.7631884172633815, 0.7631884172633811, 
  0.6461760129833164, -0.6461760129833164, -0.0827402645493758, 
  0.0827402645493757, 0.996571145790555, -0.996571145790555, 
  -0.997925286198596, 0.997925286198596, 0.06438263092985731, 
  -0.06438263092985741, -0.6601143420674206, 0.6601143420674203, 
  0.7511651319096864, -0.7511651319096865, -0.897324580705418, 
  0.897324580705418, 0.4413712687317167, -0.4413712687317167, 
  -0.3224076788010699, 0.3224076788010699, 0.946600913083284, 
  -0.946600913083284, -0.966190003445412, 0.966190003445412, 
  0.2578311021621588, -0.2578311021621589, -0.5008853826112409, 
  0.5008853826112408, 0.865513624090569, -0.865513624090569, 
  -0.7939754775543372, 0.7939754775543372, 0.6079497849677736, 
  -0.6079497849677738, -0.1315400287028833, 0.1315400287028831, 
  0.991310859846115, -0.991310859846115, -0.986809401814185, 
  0.986809401814186, 0.1618863937801118, -0.1618863937801119, 
  -0.5833086529376984, 0.5833086529376984, 0.812250586585204, 
  -0.812250586585204, -0.849741768000852, 0.849741768000852, 
  0.5271991347819011, -0.5271991347819015, -0.2280720831708858, 
  0.2280720831708857, 0.973644249650812, -0.973644249650812, 
  -0.936265667170278, 0.936265667170278, 0.351292756085567, 
  -0.3512927560855672, -0.4136383122384346, 0.4136383122384345, 
  0.910441292258067, -0.910441292258067, -0.7305627692278276, 
  0.7305627692278275, 0.682845546385248, -0.6828455463852481, 
  -0.03374117185137764, 0.03374117185137751, 0.999430604555462, 
  -0.999430604555462, -0.999204758618364, 0.999204758618364, 
  0.03987292758773972, -0.03987292758773985, -0.6783500431298616, 
  0.6783500431298613, 0.7347388780959636, -0.7347388780959636, 
  -0.907886116487666, 0.907886116487666, 0.4192168883632241, 
  -0.419216888363224, -0.3455413249639891, 0.345541324963989, 
  0.938403534063108, -0.938403534063108, -0.972226497078936, 
  0.972226497078936, 0.2340419585835433, -0.2340419585835435, 
  -0.5219752929371544, 0.5219752929371543, 0.852960604930363, 
  -0.852960604930363, -0.808656181588175, 0.808656181588175, 
  0.5882815482226453, -0.5882815482226454, -0.1558283976542653, 
  0.1558283976542652, 0.987784141644572, -0.987784141644572, 
  -0.990485084256457, 0.990485084256457, 0.1376201215864861, 
  -0.1376201215864862, -0.6030665985403483, 0.6030665985403482, 
  0.7976908409433909, -0.7976908409433912, -0.862423956111041, 
  0.862423956111041, 0.5061866453451551, -0.5061866453451555, 
  -0.2518978181542169, 0.2518978181542168, 0.967753837093476, 
  -0.967753837093476, -0.94460483726148, 0.94460483726148, 
  0.3282098435790925, -0.3282098435790926, -0.4358570799222555, 
  0.4358570799222554, 0.90001589201616, -0.90001589201616, 
  -0.7471006059801803, 0.74710060598018, 0.6647109782033449, 
  -0.6647109782033449, -0.05825826450043574, 0.05825826450043561, 
  0.998301544933893, -0.998301544933893, -0.996044700901252, 
  0.996044700901252, 0.0888535525825246, -0.0888535525825247, 
  -0.6414810128085832, 0.6414810128085831, 0.7671389119358203, 
  -0.7671389119358205, -0.886222530148881, 0.886222530148881, 
  0.4632597835518602, -0.4632597835518603, -0.2990798263080405, 
  0.2990798263080403, 0.954228095109106, -0.954228095109106, 
  -0.959571513081985, 0.959571513081985, 0.2814649379257579, 
  -0.2814649379257581, -0.4794937576601531, 0.4794937576601531, 
  0.877545290207261, -0.877545290207261, -0.778816512381476, 
  0.778816512381476, 0.6272518154951439, -0.6272518154951442, 
  -0.1071724249568089, 0.1071724249568088, 0.994240449453188, 
  -0.994240449453188, -0.982539302287441, 0.982539302287441, 
  0.1860551516634465, -0.1860551516634466, -0.5631993440138343, 
  0.5631993440138339, 0.826321062845663, -0.826321062845664, 
  -0.836547727223512, 0.836547727223512, 0.5478940591731002, 
  -0.5478940591731004, -0.204108966092817, 0.2041089660928169, 
  0.978948175319062, -0.978948175319062, -0.927362525650401, 
  0.927362525650401, 0.3741640629714579, -0.3741640629714579, 
  -0.391170384302254, 0.3911703843022539, 0.920318276709111, 
  -0.920318276709111, -0.7135848687807937, 0.7135848687807936, 
  0.7005687939432482, -0.7005687939432485, -0.00920375478205996, 
  0.00920375478205984, 0.999957644551964, -0.999957644551964};



static const double mod1024[1024] = 
{-0.999998823451702, 0.999998823451702, 0.001533980186284644, 
  -0.001533980186284766, -0.7060212614493399, 0.7060212614493395, 
  0.7081906370331953, -0.7081906370331954, -0.923291416719528, 
  0.923291416719528, 0.3841001950169349, -0.3841001950169351, 
  -0.3812657692221625, 0.3812657692221624, 0.924465474325263, 
  -0.924465474325263, -0.980484861773469, 0.980484861773469, 
  0.1965945976700801, -0.1965945976700802, -0.5542941214536202, 
  0.5542941214536201, 0.83232086776793, -0.83232086776793, 
  -0.830616400308846, 0.830616400308846, 0.5568450372751599, 
  -0.5568450372751603, -0.1935855872958037, 0.1935855872958036, 
  0.981083391150487, -0.981083391150487, -0.995033199438119, 
  0.995033199438119, 0.0995436186600693, -0.0995436186600694, 
  -0.6332067550500574, 0.6332067550500574, 0.7739826906068226, 
  -0.773982690606823, -0.881197113471222, 0.881197113471222, 
  0.4727490319503426, -0.4727490319503429, -0.2888164082060495, 
  0.2888164082060494, 0.957384500788976, -0.957384500788976, 
  -0.956493918902395, 0.956493918902395, 0.2917522632349892, 
  -0.2917522632349894, -0.4700433324595956, 0.4700433324595955, 
  0.882643339979563, -0.882643339979563, -0.7720363971503846, 
  0.7720363971503845, 0.6355783204885562, -0.6355783204885563, 
  -0.0964904313552526, 0.0964904313552525, 0.995333912140482, 
  -0.995333912140482, -0.998719012233873, 0.998719012233873, 
  0.05059974903689922, -0.05059974903689933, -0.6704215603801732, 
  0.670421560380173, 0.7419804117208308, -0.7419804117208311, 
  -0.903332368494512, 0.903332368494512, 0.4289412920553295, 
  -0.4289412920553296, -0.3354451470845317, 0.3354451470845316, 
  0.942059739771017, -0.942059739771017, -0.969657385124292, 
  0.969657385124292, 0.2444679027478241, -0.2444679027478242, 
  -0.5127864006335631, 0.5127864006335628, 0.858516224264443, 
  -0.858516224264443, -0.802292795538116, 0.802292795538116, 
  0.5969307080621965, -0.5969307080621965, -0.1452129246528475, 
  0.1452129246528474, 0.98940042779138, -0.98940042779138, 
  -0.988950264510303, 0.988950264510303, 0.1482476789868961, 
  -0.1482476789868962, -0.5944664991846646, 0.5944664991846642, 
  0.804120377398266, -0.804120377398266, -0.856938977417829, 
  0.856938977417829, 0.5154178780194629, -0.5154178780194632, 
  -0.2414918853028693, 0.2414918853028692, 0.970402838687556, 
  -0.970402838687556, -0.941026175050889, 0.941026175050889, 
  0.3383337669655412, -0.3383337669655413, -0.4261678887267996, 
  0.4261678887267997, 0.904644090578246, -0.904644090578246, 
  -0.7399200954595163, 0.7399200954595161, 0.6726947690707728, 
  -0.6726947690707731, -0.04753548415695926, 0.04753548415695914, 
  0.998869549914284, -0.998869549914284, -0.999659996743959, 
  0.999659996743959, 0.02607471782910391, -0.02607471782910404, 
  -0.6884287527840906, 0.6884287527840903, 0.7253039723730607, 
  -0.7253039723730608, -0.913587047945251, 0.913587047945251, 
  0.406643216870369, -0.4066432168703692, -0.3584634206337365, 
  0.3584634206337364, 0.933543772978836, -0.933543772978836, 
  -0.975364885116657, 0.975364885116657, 0.2205976901088735, 
  -0.2205976901088737, -0.533701001807153, 0.533701001807153, 
  0.845673246987299, -0.845673246987299, -0.816700572866828, 
  0.816700572866828, 0.5770616728556793, -0.5770616728556796, 
  -0.1694502912339679, 0.1694502912339678, 0.985538735312176, 
  -0.985538735312176, -0.992290591348257, 0.992290591348257, 
  0.1239329751185121, -0.1239329751185122, -0.6140215589310385, 
  0.6140215589310382, 0.7892892531688857, -0.7892892531688857, 
  -0.869329871348607, 0.869329871348607, 0.4942323085159598, 
  -0.4942323085159598, -0.2652340302855119, 0.2652340302855118, 
  0.964184063951746, -0.964184063951746, -0.949045881852701, 
  0.949045881852701, 0.3151379287525224, -0.3151379287525224, 
  -0.44824061228522, 0.4482406122852199, 0.893912945145203, 
  -0.893912945145203, -0.7562060014143946, 0.7562060014143945, 
  0.6543336178318003, -0.6543336178318006, -0.07203465324688941, 
  0.07203465324688931, 0.997402129901275, -0.997402129901275, 
  -0.997176436735326, 0.997176436735326, 0.07509430084792117, 
  -0.07509430084792128, -0.6520105310969596, 0.6520105310969595, 
  0.7582099098130152, -0.7582099098130153, -0.892533555402765, 
  0.892533555402765, 0.4509809890451038, -0.4509809890451038, 
  -0.3122248139218251, 0.3122248139218249, 0.950008245001843, 
  -0.950008245001843, -0.963365799780954, 0.963365799780954, 
  0.2681908570634031, -0.2681908570634031, -0.4915629161065502, 
  0.4915629161065497, 0.870842063470079, -0.870842063470079, 
  -0.7874017470290315, 0.7874017470290312, 0.6164401745308537, 
  -0.6164401745308537, -0.1208880872357772, 0.1208880872357771, 
  0.992666142448948, -0.992666142448948, -0.98501423101224, 0.98501423101224, 
  0.1724730839967959, -0.172473083996796, -0.5745533550477159, 
  0.5745533550477157, 0.818467129580299, -0.818467129580299, 
  -0.844031895490067, 0.844031895490067, 0.5362929790659631, 
  -0.5362929790659632, -0.2176042746384837, 0.2176042746384835, 
  0.976037079039039, -0.976037079039039, -0.932439629268462, 
  0.932439629268463, 0.3613258055684542, -0.3613258055684543, 
  -0.4038384575676542, 0.403838457567654, 0.914830312237946, 
  -0.914830312237946, -0.7231884893065275, 0.7231884893065275, 
  0.6906507141345344, -0.6906507141345348, -0.02300768146883941, 
  0.02300768146883929, 0.999735288260562, -0.999735288260562, 
  -0.999904701082853, 0.999904701082853, 0.01380538852806023, 
  -0.01380538852806035, -0.6972775108308867, 0.6972775108308865, 
  0.7168012785210996, -0.7168012785210996, -0.918508394325212, 
  0.918508394325212, 0.3954014789478162, -0.3954014789478163, 
  -0.3698924471489342, 0.3698924471489342, 0.929074581259316, 
  -0.929074581259316, -0.977998514934557, 0.977998514934557, 
  0.2086118519782633, -0.2086118519782634, -0.5440385267308839, 
  0.5440385267308839, 0.839060237070312, -0.839060237070313, 
  -0.823720511227391, 0.823720511227391, 0.5669960488251085, 
  -0.5669960488251088, -0.1815316082611251, 0.181531608261125, 
  0.983385110321551, -0.983385110321551, -0.993736721940725, 
  0.993736721940725, 0.1117467112111265, -0.1117467112111266, 
  -0.6236611175256947, 0.6236611175256947, 0.7816948320710592, 
  -0.7816948320710595, -0.875329403104111, 0.875329403104111, 
  0.4835270789329184, -0.4835270789329189, -0.2770460803060999, 
  0.2770460803060998, 0.96085663310768, -0.96085663310768, 
  -0.952841647601199, 0.952841647601199, 0.3034679465720113, 
  -0.3034679465720114, -0.4591765475219442, 0.4591765475219441, 
  0.888345033309596, -0.888345033309596, -0.7641787405361168, 
  0.7641787405361166, 0.6450045368155438, -0.6450045368155441, 
  -0.0842688875933241, 0.084268887593324, 0.996443051350043, 
  -0.996443051350043, -0.998022873771486, 0.998022873771486, 
  0.06285175756416131, -0.06285175756416141, -0.6612658378399923, 
  0.6612658378399922, 0.750151645806215, -0.7501516458062151, 
  -0.89800057974074, 0.89800057974074, 0.4399942713096332, 
  -0.4399942713096333, -0.323859366517853, 0.3238593665178528, 
  0.946105232370403, -0.946105232370403, -0.966584374478333, 
  0.966584374478333, 0.2563486824899428, -0.2563486824899429, 
  -0.5022124740457109, 0.5022124740457106, 0.864744257519462, 
  -0.864744257519462, -0.7949071263282371, 0.7949071263282369, 
  0.6067311270345246, -0.6067311270345246, -0.1330605251571391, 
  0.1330605251571391, 0.991107913723277, -0.991107913723277, 
  -0.987056571305751, 0.987056571305751, 0.1603724572429283, 
  -0.1603724572429284, -0.5845539429530155, 0.5845539429530151, 
  0.811354847017064, -0.811354847017064, -0.850549481265603, 
  0.850549481265603, 0.5258950274710847, -0.5258950274710849, 
  -0.2295653658205189, 0.2295653658205187, 0.973293246054698, 
  -0.973293246054698, -0.936803441735922, 0.936803441735922, 
  0.3498561297901349, -0.349856129790135, -0.4150344244760817, 
  0.4150344244760815, 0.909805708104652, -0.909805708104652, 
  -0.7316093812238927, 0.7316093812238926, 0.6817240741716497, 
  -0.6817240741716498, -0.03527423889821395, 0.03527423889821382, 
  0.999377670388003, -0.999377670388003, -0.999264747286594, 
  0.999264747286594, 0.03834012037355267, -0.03834012037355279, 
  -0.6794763198993651, 0.679476319899365, 0.7336974381146602, 
  -0.7336974381146604, -0.908528118716306, 0.908528118716306, 
  0.4178237158202123, -0.4178237158202124, -0.3469804108459237, 
  0.3469804108459236, 0.93787237643999, -0.93787237643999, 
  -0.972584368934732, 0.972584368934732, 0.2325503070387752, 
  -0.2325503070387753, -0.5232831034756565, 0.5232831034756565, 
  0.85215890162392, -0.85215890162392, -0.809557642404051, 0.809557642404051, 
  0.5870403935209178, -0.5870403935209181, -0.1573434556162383, 
  0.1573434556162382, 0.987543941794359, -0.987543941794359, 
  -0.990695025442665, 0.990695025442665, 0.1361005751757061, 
  -0.1361005751757062, -0.6042895309481561, 0.6042895309481559, 
  0.7967648102084187, -0.7967648102084189, -0.863199421712124, 
  0.863199421712124, 0.5048631085312677, -0.5048631085312677, 
  -0.2533820369955703, 0.2533820369955702, 0.967366292222328, 
  -0.967366292222328, -0.945107193285261, 0.945107193285261, 
  0.3267604523201317, -0.3267604523201317, -0.4372371736610443, 
  0.4372371736610442, 0.899346236979341, -0.899346236979341, 
  -0.7481193804504036, 0.7481193804504036, 0.6635641586120397, 
  -0.6635641586120399, -0.05978957074664001, 0.05978957074663989, 
  0.998211003360478, -0.998211003360478, -0.996179828595697, 
  0.996179828595697, 0.0873255352061921, -0.0873255352061922, 
  -0.642657033966227, 0.6426570339662269, 0.7661539901963127, 
  -0.766153990196313, -0.886932118794342, 0.886932118794342, 
  0.4618997907024626, -0.4618997907024628, -0.3005432414172734, 
  0.3005432414172733, 0.95376818988599, -0.95376818988599, 
  -0.960002145737666, 0.960002145737666, 0.2799926430802733, 
  -0.2799926430802734, -0.480839330600334, 0.4808393306003338, 
  0.876808723809146, -0.876808723809146, -0.7797777879230146, 
  0.7797777879230143, 0.6260563884043436, -0.6260563884043436, 
  -0.1086974440131387, 0.1086974440131386, 0.994074879304879, 
  -0.994074879304879, -0.982823551198705, 0.982823551198705, 
  0.1845477369386195, -0.1845477369386196, -0.5644662415205195, 
  0.5644662415205194, 0.825456154004377, -0.825456154004378, 
  -0.837387201615662, 0.837387201615662, 0.5466101669108348, 
  -0.546610166910835, -0.2056104130530993, 0.2056104130530992, 
  0.978633924429423, -0.978633924429423, -0.927935394822618, 
  0.927935394822618, 0.3727410670095157, -0.3727410670095158, 
  -0.3925816740729515, 0.3925816740729514, 0.919717146291228, 
  -0.919717146291227, -0.7146586878627691, 0.7146586878627688, 
  0.6994733446402839, -0.6994733446402839, -0.01073765916726457, 
  0.01073765916726445, 0.999942349676024, -0.999942349676024, 
  -0.999970586430974, 0.999970586430974, 0.007669828739530954, 
  -0.007669828739531078, -0.7016625947401686, 0.7016625947401685, 
  0.7125093705646921, -0.7125093705646925, -0.920917241529189, 
  0.920917241529189, 0.3897581740698563, -0.3897581740698564, 
  -0.3755861784892173, 0.3755861784892172, 0.926787474304582, 
  -0.926787474304582, -0.979260122649082, 0.979260122649082, 
  0.202607038844421, -0.2026070388444211, -0.5491766621877198, 
  0.5491766621877196, 0.835706284353753, -0.835706284353753, 
  -0.827184027273669, 0.827184027273669, 0.5619311212446894, 
  -0.5619311212446895, -0.1875621285825297, 0.1875621285825296, 
  0.982252741366289, -0.982252741366289, -0.994403680057679, 
  0.994403680057679, 0.1056471537134106, -0.1056471537134107, 
  -0.6284457666018328, 0.6284457666018327, 0.7778534042094531, 
  -0.7778534042094531, -0.878279791656541, 0.878279791656541, 
  0.478147056424843, -0.4781470564248432, -0.2829365704570554, 
  0.2829365704570553, 0.959138622461842, -0.959138622461842, 
  -0.954685754941338, 0.954685754941338, 0.2976157074350862, 
  -0.2976157074350863, -0.4646186863062379, 0.4646186863062379, 
  0.8855108561362, -0.8855108561362, -0.7681220285233655, 0.7681220285233655, 
  0.6403034821841515, -0.6403034821841518, -0.090381360877865, 
  0.0903813608778649, 0.995907229417412, -0.995907229417412, 
  -0.99838973740734, 0.99838973740734, 0.05672682116690766, 
  -0.05672682116690778, -0.6658562336655098, 0.6658562336655094, 
  0.7460800735100638, -0.7460800735100638, -0.900683429228647, 
  0.900683429228647, 0.4344759605696559, -0.4344759605696557, 
  -0.3296584625285876, 0.3296584625285874, 0.944100258491273, 
  -0.944100258491273, -0.968139104746362, 0.968139104746362, 
  0.2504130065729652, -0.2504130065729653, -0.507508991052971, 
  0.5075089910529708, 0.861646461143081, -0.861646461143081, 
  -0.798614994634761, 0.7986149946347608, 0.6018422470585799, 
  -0.6018422470585802, -0.1391393441638263, 0.1391393441638262, 
  0.990272812363169, -0.990272812363169, -0.988022017143284, 
  0.988022017143284, 0.1543129730130201, -0.1543129730130202, 
  -0.589521318641064, 0.589521318641064, 0.80775281792619, -0.80775281792619, 
  -0.853760301138111, 0.853760301138111, 0.520666254140367, 
  -0.5206662541403673, -0.2355330594049755, 0.2355330594049753, 
  0.971866337480279, -0.971866337480279, -0.938932483532065, 
  0.938932483532065, 0.3441014259899389, -0.344101425989939, 
  -0.4206090744484025, 0.4206090744484025, 0.907241977915296, 
  -0.907241977915296, -0.7357785891657136, 0.7357785891657134, 
  0.6772221701371804, -0.6772221701371805, -0.04140564097707672, 
  0.0414056409770766, 0.999142418724817, -0.999142418724817, 
  -0.999481186966167, 0.999481186966167, 0.03220802540830458, 
  -0.0322080254083047, -0.6839654117973156, 0.6839654117973155, 
  0.7295144381469969, -0.729514438146997, -0.911074734055176, 
  0.911074734055176, 0.4122412266698829, -0.412241226669883, 
  -0.3527285557552107, 0.3527285557552106, 0.93572568948108, 
  -0.93572568948108, -0.973992962167956, 0.973992962167956, 0.22657826384561, 
  -0.2265782638456101, -0.5285020015422285, 0.5285020015422283, 
  0.84893205521164, -0.84893205521164, -0.813144414849254, 0.813144414849253, 
  0.5820619903407755, -0.5820619903407756, -0.1633999493829732, 
  0.1633999493829731, 0.986559910264776, -0.986559910264776, 
  -0.991511473318744, 0.991511473318744, 0.1300192227222332, 
  -0.1300192227222333, -0.6091670123364534, 0.6091670123364531, 
  0.7930419604794436, -0.7930419604794437, -0.866280954024513, 
  0.866280954024513, 0.4995571125450818, -0.4995571125450819, 
  -0.2593129151328863, 0.2593129151328863, 0.965793358874084, 
  -0.965793358874084, -0.947094366352777, 0.947094366352777, 
  0.3209552324278751, -0.3209552324278752, -0.4427472275645702, 
  0.4427472275645699, 0.89664647017868, -0.89664647017868, 
  -0.7521768504490428, 0.7521768504490425, 0.6589612929820374, 
  -0.6589612929820374, -0.06591335279700392, 0.06591335279700381, 
  0.997825350411112, -0.997825350411112, -0.996696895202896, 
  0.996696895202896, 0.0812114468095923, -0.0812114468095924, 
  -0.6473459686365122, 0.6473459686365119, 0.7621962981345789, 
  -0.7621962981345791, -0.889749586383073, 0.889749586383073, 
  0.456448982396884, -0.4564489823968839, -0.3063897953708611, 
  0.306389795370861, 0.951906136807932, -0.951906136807932, 
  -0.961702076529123, 0.961702076529123, 0.2740969098687062, 
  -0.2740969098687063, -0.4862102761244866, 0.4862102761244865, 
  0.873841843465367, -0.873841843465367, -0.7836045186096384, 
  0.7836045186096383, 0.6212599765110875, -0.6212599765110877, 
  -0.1147949266065102, 0.1147949266065101, 0.993389211148081, 
  -0.993389211148081, -0.983937413449219, 0.983937413449219, 
  0.1785137709389974, -0.1785137709389976, -0.5695205193469473, 
  0.5695205193469473, 0.821977115279241, -0.821977115279242, 
  -0.840725374970458, 0.840725374970458, 0.5414617658531232, 
  -0.5414617658531236, -0.2116113273692276, 0.2116113273692275, 
  0.9773539001452, -0.9773539001452, -0.930205022892219, 0.930205022892219, 
  0.3670403457197671, -0.3670403457197672, -0.3982175621533736, 
  0.3982175621533735, 0.917290997008378, -0.917290997008378, 
  -0.7189371223728046, 0.7189371223728043, 0.6950751139800008, 
  -0.6950751139800009, -0.01687298794728177, 0.01687298794728165, 
  0.999857641005824, -0.999857641005824, -0.999801169887884, 
  0.999801169887884, 0.01994042855151448, -0.0199404285515146, 
  -0.6928661748174248, 0.6928661748174246, 0.7210661993145079, 
  -0.7210661993145081, -0.916064965799332, 0.916064965799332, 
  0.4010298971835757, -0.4010298971835759, -0.3641847895670798, 
  0.3641847895670797, 0.93132670908118, -0.93132670908118, 
  -0.976700086128712, 0.976700086128712, 0.2146088109937868, 
  -0.2146088109937869, -0.5388799085310084, 0.5388799085310083, 
  0.842382599643186, -0.842382599643186, -0.820225982569435, 
  0.820225982569434, 0.5720396293247571, -0.5720396293247572, 
  -0.1754942533772714, 0.1754942533772712, 0.984480455383221, 
  -0.984480455383221, -0.993032350197851, 0.993032350197851, 
  0.1178420615083249, -0.117842061508325, -0.6188529879609765, 
  0.6188529879609762, 0.7855068295640538, -0.7855068295640539, 
  -0.872346058894392, 0.872346058894392, 0.4888888969197631, 
  -0.4888888969197632, -0.271145159526808, 0.2711451595268079, 
  0.962538468044359, -0.962538468044359, -0.950961666311575, 
  0.950961666311575, 0.3093087603122687, -0.3093087603122687, 
  -0.4537171210001639, 0.4537171210001637, 0.891145764794583, 
  -0.891145764794583, -0.7602066816512025, 0.7602066816512023, 
  0.6496813073906833, -0.6496813073906833, -0.07815324163279431, 
  0.07815324163279419, 0.996941357764982, -0.996941357764982, 
  -0.99761843513852, 0.997618435138519, 0.06897432762826662, 
  -0.06897432762826674, -0.6566505457294291, 0.6566505457294288, 
  0.7541949753168892, -0.7541949753168894, -0.895283921038558, 
  0.895283921038557, 0.4454960165139818, -0.4454960165139818, 
  -0.318048077385015, 0.3180480773850149, 0.948074585922276, 
  -0.948074585922276, -0.96499325285492, 0.96499325285492, 
  0.2622747070239135, -0.2622747070239136, -0.4968970490226547, 
  0.4968970490226545, 0.867809496763303, -0.867809496763303, 
  -0.7911693302176902, 0.7911693302176901, 0.6115971639264619, 
  -0.611597163926462, -0.126976696496886, 0.1269766964968859, 
  0.991905700430609, -0.991905700430609, -0.986053963346195, 
  0.986053963346195, 0.1664259035404641, -0.1664259035404642, 
  -0.5795645591394058, 0.5795645591394058, 0.814926329056526, 
  -0.814926329056527, -0.847306638685858, 0.847306638685858, 
  0.5311040011512547, -0.5311040011512552, -0.22358902922979, 
  0.2235890292297899, 0.974683510688511, -0.974683510688511, 
  -0.934639129819681, 0.934639129819681, 0.3555976617047838, 
  -0.355597661704784, -0.4094441486922576, 0.4094441486922575, 
  0.912335184623323, -0.912335184623323, -0.7274126286023758, 
  0.7274126286023757, 0.6862003116800385, -0.6862003116800387, 
  -0.02914150876419374, 0.02914150876419362, 0.999575296046749, 
  -0.999575296046749, -0.999010685854073, 0.999010685854073, 
  0.04447077185493863, -0.04447077185493875, -0.6749616461020121, 
  0.6749616461020121, 0.7378528147884658, -0.7378528147884662, 
  -0.905947297807268, 0.905947297807268, 0.4233904741437958, 
  -0.4233904741437961, -0.3412192023202824, 0.3412192023202823, 
  0.939983753034014, -0.939983753034014, -0.971139158449725, 
  0.971139158449725, 0.2385135948443184, -0.2385135948443185, 
  -0.5180445040959995, 0.5180445040959993, 0.855353664735196, 
  -0.855353664735196, -0.805940390571177, 0.805940390571176, 
  0.5919966949620409, -0.591996694962041, -0.1512810379573302, 
  0.1512810379573301, 0.988490792852697, -0.988490792852697, 
  -0.98984127845882, 0.98984127845882, 0.1421768035194479, 
  -0.142176803519448, -0.5993892984005647, 0.5993892984005646, 
  0.800457662192623, -0.800457662192623, -0.86008539042939, 0.86008539042939, 
  0.5101500967067666, -0.5101500967067669, -0.2474416191677734, 
  0.2474416191677733, 0.968902804776429, -0.968902804776429, 
  -0.943084437466093, 0.943084437466093, 0.3325533698660441, 
  -0.3325533698660442, -0.4317106580250574, 0.4317106580250571, 
  0.902012143902493, -0.902012143902493, -0.7440337441799293, 
  0.7440337441799291, 0.6681420414265185, -0.6681420414265186, 
  -0.05366353765273068, 0.05366353765273056, 0.998559074229759, 
  -0.998559074229759, -0.995625256380994, 0.995625256380994, 
  0.0934363358457478, -0.0934363358457479, -0.6379439036218442, 
  0.637943903621844, 0.7700828369933479, -0.770082836993348, 
  -0.884081258712635, 0.884081258712635, 0.4673332087419884, 
  -0.4673332087419885, -0.2946853721805143, 0.2946853721805142, 
  0.955594334130771, -0.955594334130771, -0.958266071408018, 
  0.958266071408018, 0.2858778347270806, -0.2858778347270807, 
  -0.4754502817471559, 0.475450281747156, 0.879742592800047, 
  -0.879742592800048, -0.7759216990434077, 0.7759216990434077, 
  0.6308292296284244, -0.6308292296284246, -0.1025958690224363, 
  0.1025958690224362, 0.994723121104326, -0.994723121104326, 
  -0.981672686196983, 0.981672686196983, 0.1905747548202526, 
  -0.1905747548202528, -0.5593907118591362, 0.5593907118591358, 
  0.828904114771865, -0.828904114771865, -0.834017501106018, 
  0.834017501106018, 0.5517379884047075, -0.5517379884047075, 
  -0.199601757621131, 0.1996017576211309, 0.979877103699518, 
  -0.979877103699518, -0.925630830509873, 0.925630830509873, 
  0.3784277548087655, -0.3784277548087656, -0.3869310055143887, 
  0.3869310055143886, 0.922108668743345, -0.922108668743345, 
  -0.7103533468570625, 0.7103533468570623, 0.7038452405244849, 
  -0.7038452405244851, -0.004601926120448672, 0.004601926120448549, 
  0.999989411081928, -0.999989411081928};

static const double mod2048[2048] = 
{-0.999999705862882, 0.999999705862882, 0.000766990318742724, 
  -0.0007669903187428464, -0.7065642291447097, 0.7065642291447095, 
  0.7076489172556844, -0.7076489172556844, -0.923585746276257, 
  0.923585746276257, 0.3833919264608086, -0.3833919264608088, 
  -0.3819747131465672, 0.3819747131465671, 0.924172775251791, 
  -0.924172775251791, -0.980635359529608, 0.980635359529608, 
  0.1958425174476579, -0.195842517447658, -0.5549323404628105, 
  0.5549323404628104, 0.831895484726578, -0.831895484726578, 
  -0.831043250746362, 0.831043250746362, 0.5562077987487398, 
  -0.5562077987487401, -0.1943380118179886, 0.1943380118179885, 
  0.980934624306142, -0.980934624306142, -0.995109255753726, 
  0.995109255753726, 0.0987804085497995, -0.0987804085497996, 
  -0.6338002060310173, 0.633800206031017, 0.7734967994988992, 
  -0.7734967994988992, -0.881559448209144, 0.881559448209144, 
  0.4720730232423688, -0.4720730232423687, -0.2895506278978432, 
  0.289550627897843, 0.95716269979767, -0.95716269979767, -0.956717408723403, 
  0.956717408723403, 0.291018555844085, -0.2910185558440851, 
  -0.4707201730990718, 0.4707201730990717, 0.882282561676009, 
  -0.882282561676009, -0.7725236524844413, 0.7725236524844413, 
  0.6349859890990494, -0.6349859890990496, -0.0972538144483634, 
  0.0972538144483633, 0.995259612149133, -0.995259612149133, 
  -0.998757527991183, 0.998757527991183, 0.04983372634010714, 
  -0.04983372634010726, -0.6709904549767943, 0.6709904549767943, 
  0.7414659866305631, -0.7414659866305633, -0.903661096609248, 
  0.903661096609248, 0.4282483187065318, -0.4282483187065319, 
  -0.3361675991177446, 0.3361675991177446, 0.941802179495998, 
  -0.941802179495998, -0.969844604426715, 0.969844604426715, 
  0.243724113013852, -0.2437241130138521, -0.5134447234365436, 
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  0.7000212751940062, 0.7141219883715647, -0.7141219883715648, 
  -0.920017982111607, 0.920017982111606, 0.3918761444529222, 
  -0.3918761444529224, -0.3734526748367804, 0.3734526748367803, 
  0.927649233092581, -0.927649233092581, -0.978791337773106, 
  0.978791337773106, 0.2048597498298143, -0.2048597498298144, 
  -0.5472522740091741, 0.5472522740091741, 0.836967710602857, 
  -0.836967710602857, -0.825888851349587, 0.825888851349587, 
  0.563832958611378, -0.5638329586113783, -0.185301498805082, 
  0.1853014988050819, 0.982681715786241, -0.982681715786241, 
  -0.99415795679779, 0.99415795679779, 0.1079349662326537, 
  -0.1079349662326537, -0.6266542862720295, 0.6266542862720295, 
  0.7792973793725301, -0.7792973793725304, -0.877177265018596, 
  0.877177265018596, 0.4801666853650881, -0.4801666853650885, 
  -0.2807288730757972, 0.2807288730757971, 0.95978711171884, 
  -0.95978711171884, -0.953998423103895, 0.953998423103895, 
  0.2998116220483833, -0.2998116220483835, -0.4625799231890868, 
  0.4625799231890868, 0.886577585246987, -0.886577585246987, 
  -0.7666466765653106, 0.7666466765653103, 0.6420692122437925, 
  -0.6420692122437927, -0.0880895698047705, 0.0880895698047704, 
  0.996112557742151, -0.996112557742151, -0.998256567771495, 
  0.998256567771495, 0.05902393498466786, -0.05902393498466799, 
  -0.6641377637552601, 0.66413776375526, 0.7476102131152051, 
  -0.7476102131152053, -0.899681329127424, 0.899681329127424, 
  0.4365472551964011, -0.4365472551964013, -0.3274852442751781, 
  0.3274852442751779, 0.944856293190677, -0.944856293190677, 
  -0.967560349253315, 0.967560349253314, 0.2526400018856955, 
  -0.2526400018856956, -0.5055250256318855, 0.5055250256318851, 
  0.8628119426966, -0.8628119426966, -0.7972280600702688, 0.7972280600702685, 
  0.6036782423084305, -0.6036782423084305, -0.1368603886368164, 
  0.1368603886368163, 0.99059034621895, -0.99059034621895, 
  -0.987664332228206, 0.987664332228206, 0.1565859726929985, 
  -0.1565859726929986, -0.5876611437247368, 0.5876611437247366, 
  0.809107149984558, -0.809107149984558, -0.852560004046684, 
  0.852560004046684, 0.5226293519310966, -0.5226293519310969, 
  -0.2332962014322315, 0.2332962014322315, 0.97240571902745, 
  -0.97240571902745, -0.938138231192824, 0.938138231192824, 0.34626096975316, 
  -0.3462609697531601, -0.4185204251941097, 0.4185204251941098, 
  0.908207384739489, -0.908207384739489, -0.7342183740661883, 
  0.7342183740661882, 0.6789133812082382, -0.6789133812082385, 
  -0.03910653548332985, 0.03910653548332972, 0.999235046864596, 
  -0.999235046864596, -0.999404431433671, 0.999404431433671, 
  0.03450771552479576, -0.03450771552479589, -0.6822850109637957, 
  0.6822850109637955, 0.7310862902654743, -0.7310862902654744, 
  -0.910123767882542, 0.910123767882542, 0.4143364902289992, 
  -0.4143364902289992, -0.3505745460548375, 0.3505745460548375, 
  0.936534829922756, -0.936534829922756, -0.973469034186131, 
  0.973469034186131, 0.2288187917998022, -0.2288187917998024, 
  -0.5265472360035794, 0.5265472360035794, 0.850145874692685, 
  -0.850145874692685, -0.811802955582516, 0.811802955582515, 
  0.5839314697012761, -0.5839314697012763, -0.1611294729056788, 
  0.1611294729056787, 0.986933276853678, -0.986933276853678, 
  -0.991209678336254, 0.991209678336254, 0.1323003158444446, 
  -0.1323003158444447, -0.607340634642573, 0.6073406346425726, 
  0.7944415356160306, -0.7944415356160306, -0.865129195271624, 
  0.865129195271624, 0.5015490758526754, -0.5015490758526754, 
  -0.2570899679457532, 0.2570899679457531, 0.966387473212299, 
  -0.966387473212299, -0.946353351084491, 0.946353351084491, 
  0.3231336177050522, -0.3231336177050523, -0.440682899641873, 
  0.4406828996418729, 0.897662844259041, -0.897662844259041, 
  -0.7506586096545107, 0.7506586096545105, 0.6606902842872423, 
  -0.6606902842872424, -0.0636172129591932, 0.06361721295919308, 
  0.997974373526347, -0.997974373526347, -0.996507391680111, 
  0.996507391680111, 0.0835046006331523, -0.0835046006331524, 
  -0.6455904647915488, 0.6455904647915487, 0.7636838035275018, 
  -0.763683803527502, -0.888696955980892, 0.888696955980892, 
  0.4584950604208262, -0.4584950604208263, -0.3041986776298293, 
  0.3041986776298291, 0.952608610358033, -0.952608610358033, 
  -0.961068842145519, 0.961068842145519, 0.2763090310812709, 
  -0.276309031081271, -0.4841983058875492, 0.4841983058875489, 
  0.874958285048852, -0.874958285048852, -0.782172944184913, 
  0.7821729441849128, 0.6230613817154013, -0.6230613817154014, 
  -0.1125088647873788, 0.1125088647873787, 0.993650721000219, 
  -0.993650721000219, -0.983524054057571, 0.983524054057571, 
  0.1807773080067286, -0.1807773080067287, -0.5676276677079864, 
  0.5676276677079862, 0.8232853884604, -0.8232853884604, -0.839477262554579, 
  0.839477262554578, 0.5433948156302847, -0.5433948156302849, 
  -0.2093619060104742, 0.2093619060104741, 0.97783822399805, 
  -0.97783822399805, -0.929358011909936, 0.929358011909936, 0.36917974714062, 
  -0.36917974714062, -0.3961058496916963, 0.3961058496916962, 
  0.918204855051431, -0.918204855051431, -0.7173358727835218, 
  0.7173358727835218, 0.6967275260946009, -0.6967275260946013, 
  -0.0145723016927791, 0.01457230169277898, 0.999893818374419, 
  -0.999893818374419, -0.999752640870249, 0.999752640870249, 
  0.02224088741402479, -0.02224088741402492, -0.6912051895584486, 
  0.6912051895584482, 0.7226585541785756, -0.7226585541785758, 
  -0.915139783339685, 0.915139783339685, 0.4031366727909952, 
  -0.4031366727909952, -0.3620408714575843, 0.3620408714575842, 
  0.932162221608575, -0.932162221608575, -0.976203692322271, 
  0.976203692322271, 0.2168555996426325, -0.2168555996426326, 
  -0.5369401856148432, 0.536940185614843, 0.843620315706004, 
  -0.843620315706004, -0.818907565699659, 0.818907565699659, 
  0.5739254296856506, -0.5739254296856508, -0.1732285296450705, 
  0.1732285296450704, 0.984881656097324, -0.984881656097324, 
  -0.992758570461551, 0.992758570461551, 0.1201266863571015, 
  -0.1201266863571016, -0.6170439227298498, 0.6170439227298498, 
  0.7869287117790016, -0.7869287117790018, -0.871218831320811, 
  0.871218831320811, 0.4908948440878148, -0.4908948440878153, 
  -0.2689296704203573, 0.2689296704203572, 0.963159816628371, 
  -0.963159816628371, -0.950247438978705, 0.950247438978705, 
  0.3114960749582758, -0.311496074958276, -0.4516654209910026, 
  0.4516654209910025, 0.892187394822983, -0.892187394822983, 
  -0.7587097725604074, 0.7587097725604073, 0.6514287996560597, 
  -0.6514287996560598, -0.07585910343295449, 0.07585910343295438, 
  0.99711854682698, -0.99711854682698, -0.997457086409942, 0.997457086409942, 
  0.07126963428129631, -0.07126963428129641, -0.6549134280500562, 
  0.6549134280500561, 0.7557039114360358, -0.755703911436036, 
  -0.894256478422316, 0.894256478422316, 0.4475548578662929, 
  -0.447554857866293, -0.3158657450621841, 0.315865745062184, 
  0.948803894962658, -0.948803894962658, -0.964387212282854, 
  0.964387212282854, 0.2644944324278015, -0.2644944324278016, 
  -0.4948989307390114, 0.4948989307390109, 0.868950544250582, 
  -0.868950544250582, -0.7897599696008192, 0.7897599696008189, 
  0.6134160011086387, -0.6134160011086387, -0.1246940159421678, 
  0.1246940159421676, 0.992195244086674, -0.992195244086674, 
  -0.985668412161538, 0.985668412161538, 0.1686943427236173, 
  -0.1686943427236174, -0.577687904553123, 0.5776879045531226, 
  0.816257731928477, -0.816257731928478, -0.846082341744897, 
  0.846082341744897, 0.5330522216326195, -0.5330522216326197, 
  -0.2213457206470308, 0.2213457206470307, 0.97519540193299, 
  -0.97519540193299, -0.933818436362211, 0.933818436362211, 
  0.3577472961603419, -0.3577472961603419, -0.407343809682608, 
  0.4073438096826079, 0.913274887814868, -0.913274887814868, 
  -0.7258317772227704, 0.7258317772227703, 0.6878722491666853, 
  -0.6878722491666856, -0.02684143969909853, 0.02684143969909841, 
  0.99963970365071, -0.99963970365071, -0.998905715365818, 0.998905715365818, 
  0.04676934690053784, -0.04676934690053797, -0.6732620827561331, 
  0.6732620827561329, 0.7394039274462056, -0.7394039274462059, 
  -0.904970691133653, 0.904970691133653, 0.4254739101156238, 
  -0.4254739101156239, -0.3390554254149696, 0.3390554254149695, 
  0.940766399536396, -0.940766399536396, -0.970587775194143, 
  0.970587775194144, 0.2407475246885884, -0.2407475246885885, 
  -0.5160749903153668, 0.5160749903153668, 0.85654340483772, 
  -0.85654340483772, -0.804576090926307, 0.804576090926307, 
  0.5938495717854333, -0.5938495717854337, -0.1490061506603485, 
  0.1490061506603484, 0.988836269088764, -0.988836269088764, 
  -0.989511513679355, 0.989511513679355, 0.1444540213908603, 
  -0.1444540213908604, -0.5975458832896933, 0.5975458832896931, 
  0.801834719479981, -0.801834719479981, -0.858909273947824, 
  0.858909273947824, 0.5121277761715547, -0.5121277761715547, 
  -0.2452115486676277, 0.2452115486676276, 0.969469595397413, 
  -0.969469595397413, -0.942316745856564, 0.942316745856564, 
  0.3347224977175811, -0.3347224977175812, -0.4296340130690166, 
  0.4296340130690164, 0.903003108972617, -0.903003108972617, 
  -0.7424944003231393, 0.7424944003231392, 0.6698522713918209, 
  -0.6698522713918212, -0.05136574196716273, 0.05136574196716261, 
  0.998679908955899, -0.998679908955899, -0.995407626602535, 
  0.995407626602535, 0.0957269914993072, -0.0957269914993073, 
  -0.6361702779837123, 0.6361702779837123, 0.7715486876472062, 
  -0.7715486876472064, -0.883003599046781, 0.883003599046781, 
  0.4693662153057374, -0.4693662153057377, -0.2924857989955538, 
  0.2924857989955537, 0.956269866400658, -0.956269866400658, 
  -0.957605738575646, 0.957605738575646, 0.2880820186110042, 
  -0.2880820186110043, -0.4734247625522415, 0.4734247625522415, 
  0.880834260347742, -0.880834260347742, -0.7744681264006709, 
  0.7744681264006707, 0.6326129315698774, -0.6326129315698776, 
  -0.1003067702113928, 0.1003067702113927, 0.994956557770116, 
  -0.994956557770116, -0.98123158084875, 0.98123158084875, 
  0.1928330488922052, -0.1928330488922052, -0.5574819482239917, 
  0.5574819482239915, 0.830189061241102, -0.830189061241102, 
  -0.83274576117636, 0.832745761176359, 0.5536555763674792, 
  -0.5536555763674793, -0.197346562240966, 0.1973465622409659, 
  0.980333787223348, -0.980333787223348, -0.924757629559514, 
  0.924757629559514, 0.3805566010089285, -0.3805566010089286, 
  -0.3848082376168129, 0.3848082376168128, 0.922996544014246, 
  -0.922996544014246, -0.7087319402004008, 0.7087319402004005, 
  0.7054778784198522, -0.7054778784198522, -0.002300969151425886, 
  0.002300969151425764, 0.999997352766978, -0.999997352766978};


static const double mod4096[4096] = 
{-0.999999926465718, 0.999999926465718, 0.0003834951875713746, 
  -0.0003834951875714971, -0.7068355571422739, 0.7068355571422739, 
  0.7073779012376419, -0.7073779012376422, -0.923732707319793, 
  0.923732707319793, 0.3830377075793521, -0.3830377075793521, 
  -0.3823291008701245, 0.3823291008701244, 0.924026221829144, 
  -0.924026221829144, -0.980710392082254, 0.980710392082254, 
  0.1954664341053769, -0.1954664341053771, -0.5552513275712141, 
  0.555251327571214, 0.831682609671745, -0.831682609671745, 
  -0.831256492650303, 0.831256492650303, 0.5558890567610738, 
  -0.5558890567610739, -0.194714181235226, 0.1947141812352259, 
  0.980860024481524, -0.980860024481524, -0.995147064390386, 
  0.995147064390386, 0.0983987816753638, -0.0983987816753639, 
  -0.6340967917251838, 0.6340967917251838, 0.7732536832914724, 
  -0.7732536832914727, -0.881740421116898, 0.881740421116898, 
  0.4717349147228714, -0.4717349147228715, -0.2899176738950409, 
  0.2899176738950407, 0.957051588141041, -0.957051588141041, 
  -0.956828942587535, 0.956828942587535, 0.2906516379221331, 
  -0.2906516379221332, -0.4710584896014826, 0.4710584896014823, 
  0.882101977876918, -0.882101977876918, -0.7727671097484638, 
  0.7727671097484637, 0.6346896833027978, -0.6346896833027979, 
  -0.0976354845685173, 0.0976354845685172, 0.995222242593618, 
  -0.995222242593618, -0.998776565542496, 0.998776565542496, 
  0.0494507039700847, -0.04945070397008483, -0.6712747542736137, 
  0.6712747542736133, 0.7412086104970043, -0.7412086104970044, 
  -0.903825261328487, 0.903825261328487, 0.4279017375338542, 
  -0.4279017375338542, -0.3365287510013823, 0.3365287510013823, 
  0.941673191584771, -0.941673191584771, -0.969938000134324, 
  0.969938000134324, 0.2433521643532848, -0.2433521643532849, 
  -0.5137737715948681, 0.5137737715948681, 0.85792570285613, 
  -0.85792570285613, -0.802979024600843, 0.802979024600843, 
  0.5960072869110564, -0.5960072869110567, -0.1463511192344114, 
  0.1463511192344113, 0.98923270765722, -0.98923270765722, 
  -0.989120166795573, 0.989120166795573, 0.1471098080968717, 
  -0.1471098080968718, -0.5953912344651688, 0.5953912344651684, 
  0.803435920233868, -0.803435920233868, -0.857531390999499, 
  0.857531390999499, 0.514431641183223, -0.514431641183223, 
  -0.2426081597184969, 0.2426081597184968, 0.97012436359366, 
  -0.97012436359366, -0.941414800309736, 0.941414800309736, 
  0.3372509062371505, -0.3372509062371507, -0.4272083864467965, 
  0.4272083864467963, 0.904153191969992, -0.904153191969992, 
  -0.7406935312422958, 0.7406935312422956, 0.6718430566552119, 
  -0.6718430566552121, -0.04868463746843902, 0.0486846374684389, 
  0.998814199976435, -0.998814199976435, -0.999689333741033, 
  0.999689333741034, 0.02492460640428136, -0.02492460640428149, 
  -0.6892627487612736, 0.6892627487612733, 0.7245114651750196, 
  -0.7245114651750196, -0.914054280384047, 0.914054280384046, 
  0.4055918792476038, -0.4055918792476039, -0.3595372118219732, 
  0.3595372118219731, 0.933130748242325, -0.933130748242325, 
  -0.975618034019782, 0.975618034019782, 0.2194754011167902, 
  -0.2194754011167903, -0.5346735832699557, 0.5346735832699555, 
  0.845058672136596, -0.845058672136596, -0.817363933360699, 
  0.817363933360698, 0.5761216889174783, -0.5761216889174784, 
  -0.1705840269544637, 0.1705840269544636, 0.985343132998855, 
  -0.985343132998855, -0.992432517712594, 0.992432517712594, 
  0.1227912773231168, -0.1227912773231169, -0.6149292182788797, 
  0.6149292182788796, 0.788582308010347, -0.7885823080103473, 
  -0.869897903042807, 0.869897903042807, 0.4932318301587278, 
  -0.4932318301587281, -0.2663431343792382, 0.266343134379238, 
  0.963878277983814, -0.963878277983814, -0.949407815332292, 
  0.949407815332292, 0.3140458568202507, -0.3140458568202508, 
  -0.44926874937183, 0.4492687493718299, 0.893396659294108, 
  -0.893396659294108, -0.7569583021837506, 0.7569583021837504, 
  0.6534631808718024, -0.6534631808718025, -0.07318210209940288, 
  0.07318210209940278, 0.997318594999769, -0.997318594999769, 
  -0.997262171687536, 0.997262171687536, 0.07394701428089716, 
  -0.07394701428089727, -0.652882408974559, 0.6528824089745589, 
  0.7574592794676006, -0.7574592794676008, -0.893051811731707, 
  0.893051811731707, 0.4499538438136905, -0.4499538438136906, 
  -0.313317577844809, 0.313317577844809, 0.949648406208036, 
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  0.4041892608938708, -0.4041892608938708, -0.3609681928880952, 
  0.3609681928880952, 0.932578127409764, -0.932578127409764, 
  -0.975953557074734, 0.975953557074734, 0.2179785641598122, 
  -0.2179785641598123, -0.5359692574599668, 0.5359692574599668, 
  0.844237499201387, -0.844237499201387, -0.818246730948242, 
  0.818246730948242, 0.5748671910037264, -0.5748671910037268, 
  -0.172095323096829, 0.1720953230968289, 0.985080301177624, 
  -0.985080301177624, -0.992619709454266, 0.992619709454266, 
  0.1212687610348524, -0.1212687610348526, -0.616138164420697, 
  0.6161381644206968, 0.7876380909683675, -0.7876380909683675, 
  -0.870653487420617, 0.870653487420617, 0.4918968437002994, 
  -0.4918968437002994, -0.2678213911940943, 0.2678213911940942, 
  0.963468578843576, -0.963468578843576, -0.949888438430089, 
  0.949888438430089, 0.3125891145527086, -0.3125891145527087, 
  -0.4506386735592978, 0.4506386735592977, 0.892706438809935, 
  -0.892706438809935, -0.7579598111576723, 0.7579598111576722, 
  0.6523012530034153, -0.6523012530034155, -0.07471188296126837, 
  0.07471188296126825, 0.997205161711662, -0.997205161711662, 
  -0.997374431615167, 0.997374431615167, 0.07241714686676343, 
  -0.07241714686676354, -0.6540435683534928, 0.6540435683534927, 
  0.7564568796008336, -0.7564568796008338, -0.893740981294271, 
  0.893740981294271, 0.4485833906367391, -0.4485833906367393, 
  -0.3147739510506061, 0.314773951050606, 0.949166665944391, 
  -0.949166665944391, -0.964082277076968, 0.964082277076968, 
  0.2656037707301763, -0.2656037707301764, -0.4938988883508675, 
  0.4938988883508673, 0.869519343134917, -0.869519343134917, 
  -0.7890537208161521, 0.7890537208161518, 0.614324202409596, 
  -0.614324202409596, -0.1235524273387353, 0.1235524273387353, 
  0.99233804608042, -0.99233804608042, -0.985473679470072, 0.985473679470072, 
  0.1698282281357198, -0.1698282281357199, -0.5767484296824826, 
  0.5767484296824823, 0.816921813185809, -0.81692181318581, 
  -0.845468513035529, 0.845468513035529, 0.5340252741823103, 
  -0.5340252741823105, -0.2202236261478125, 0.2202236261478124, 
  0.975449411546446, -0.975449411546446, -0.933406235334632, 
  0.933406235334632, 0.3588214038187108, -0.3588214038187108, 
  -0.4062928307318375, 0.4062928307318374, 0.913742926482011, 
  -0.913742926482011, -0.7250399099246754, 0.7250399099246751, 
  0.6887068527439079, -0.6887068527439079, -0.0256913511137594, 
  0.02569135111375927, 0.999669922763484, -0.999669922763484, 
  -0.998851246833715, 0.998851246833715, 0.0479185423268752, 
  -0.04791854232687533, -0.6724109638088499, 0.6724109638088498, 
  0.7401780162566661, -0.7401780162566663, -0.904480590721468, 
  0.904480590721468, 0.4265147840440515, -0.4265147840440516, 
  -0.3379728630768998, 0.3379728630768997, 0.941155855224629, 
  -0.941155855224629, -0.970310156353828, 0.970310156353828, 
  0.2418640123635791, -0.2418640123635792, -0.5150892081446975, 
  0.5150892081446969, 0.857136574679245, -0.857136574679245, 
  -0.803892343226241, 0.803892343226241, 0.5947748317659576, 
  -0.5947748317659576, -0.1478684104184223, 0.1478684104184222, 
  0.989007044060015, -0.989007044060015, -0.989344666578753, 
  0.989344666578753, 0.1455923442773583, -0.1455923442773585, 
  -0.5966229887412134, 0.5966229887412132, 0.802521656595946, 
  -0.802521656595946, -0.858319510017173, 0.858319510017173, 
  0.5131155997666405, -0.5131155997666407, -0.2440960258302642, 
  0.2440960258302641, 0.969751066085452, -0.969751066085452, 
  -0.94193102889773, 0.94193102889773, 0.3358063977944204, 
  -0.3358063977944206, -0.4285948368973444, 0.4285948368973445, 
  0.903496798989868, -0.903496798989868, -0.7417232537177842, 
  0.7417232537177842, 0.6707060569983719, -0.6707060569983722, 
  -0.05021674138115533, 0.0502167413811552, 0.998738343554035, 
  -0.998738343554035, -0.995296835333246, 0.995296835333246, 
  0.0968721300252304, -0.0968721300252305, -0.6352822015088236, 
  0.6352822015088232, 0.7722800816064744, -0.7722800816064744, 
  -0.88246301571907, 0.88246301571907, 0.4703817873685209, 
  -0.4703817873685207, -0.2913854309663557, 0.2913854309663556, 
  0.956605734156215, -0.956605734156215, -0.957273670685755, 
  0.957273670685755, 0.2891835393168502, -0.2891835393168502, 
  -0.4724110623347641, 0.4724110623347641, 0.881378345651707, 
  -0.881378345651707, -0.7737398019492618, 0.7737398019492617, 
  0.6335035271247643, -0.6335035271247645, -0.0991620208967426, 
  0.0991620208967425, 0.995071300767776, -0.995071300767776, 
  -0.981009079866113, 0.981009079866113, 0.1939618138197389, 
  -0.193961813819739, -0.5565264589357238, 0.5565264589357236, 
  0.830829886622083, -0.830829886622084, -0.832108237435736, 
  0.832108237435735, 0.5546132717413039, -0.5546132717413041, 
  -0.1962185719876608, 0.1962185719876607, 0.980560182756328, 
  -0.980560182756328, -0.924319192757675, 0.924319192757675, 
  0.3816202692465374, -0.3816202692465374, -0.383746088957365, 
  0.3837460889573649, 0.92343864940229, -0.92343864940229, 
  -0.7079198292008164, 0.7079198292008161, 0.7062927972337585, 
  -0.7062927972337585, -0.001150485337113809, 0.001150485337113686, 
  0.999999338191526, -0.999999338191526};

/*** "interface" to the above arrays ***/

/************************************************************************

  get supermoduli lists

  These are the values of the T0 components of the supermoduli in the
  proper order.

  ************************************************************************/
const double *get_mods(int n)
{
  switch(n)
    {
    case 2: return mod2;
    case 4: return mod4;
    case 8: return mod8;
    case 16: return mod16;
    case 32: return mod32;
    case 64: return mod64;
    case 128: return mod128;
    case 256: return mod256;
    case 512: return mod512;
    case 1024: return mod1024;
    case 2048: return mod2048;
    case 4096: return mod4096;
    default: return 0 ;
    }
} 
